Determination of optimum Hargreaves-Samani equation for Mediterranean region

Abstract

Penman-Monteith equation is the most commonly used model in the literature for estimation of reference (grass) evapotranspiration (ET0) because of the fact that it gives more accurate and consistent estimates. Despite its higher accuracy potential, Penman-Monteith equation requires quite a few meteorological quantities as explanatory variables affecting the value of evapotranspiration such as solar radiation, air temperature, wind velocity, and relative humidity. Because it needs so many meteorological variables and partly due to its cumbersome analytical form, the Penman-Monteith (PM) equation is not easily applicable for all cases for calculating the reference evapotranspiration, and therefore the Hargreaves-Samani (HS) equation is necessarily used instead of it for regions at which the pertinent meteorological data may not be available. Originally, the HS equation was developed for semiarid environments, therefore, its results are less accurate as compared to the FAO-56 PM formula for different climate conditions. For this reason, many researchers tried to calibrate the HS equation based on the FAO-56 PM with different methods. Generally, the main approach for the calibration of the HS equation is linear regression with PM ET0 or lysimeter values. . Alternatively, some researchers were calibrated the HS equation by adjusting the constant values of the HS equation. In addition to these methods, different numerous attempts were done for improving the estimation capability of the HS equation with the help of additional climatic variables such as wind speed (WS), relative humidity (RH). Various studies have shown that this method overestimates ET0 in warm humid areas. In this study, first, Hargreaves-Samani equation is calibrated using maximum temperature, minimum temperature, maximum humidity and minimum humidity data measured at 38 stations in the highly humid Mediterranean Region of Turkey. Using the monthly average values of the relevant meteorological variables and ET0,PM values over the period: 1975–2010 were used for the calibration (training phase) and validation (testing phase) of the HS equation. With the help of Excel Solver, suitable magnitudes for a and b coefficients of the HS equation for different meteorological variables (RHmax, RHmin, Tmax and Tmin) were computed based on the ET0 values computed by the FAO-56 PM equation. The predictive abilities of the HS equation calibration in such manner were quantitatively evaluated by the common test statistics. For reliability assessment of calibrated HS equations, 3 weather stations data were used for regions. The results of the original and calibrated HS equations data were compared. A reduction in the mean absolute relative error (MARE), root mean square error (RMSE) and mean absolute error (MAE) statistics are obtained with calibrated HS equations. The scatter diagram of the FAO-56 PM equation versus original and calibrated HS equations show that the calibrated HS equations estimates are closer to the exact line (1:1 line). The calibrated HS equation reduces the MARE statistics almost 3% and 10% for the training and testing data sets, respectively. The best estimations obtained from calibration with the maximum temperature, which provided the smallest values of MAE (0.849 and 0.704 mm), MARE (14.76 and 10.56%) and RMSE (1.143 and 0.904 mm) according to training and testing datasets, respectively. In conclusion, it is observed that the calculated evapotranspiration values using calibrated Hargreaves-Samani equation are close to those calculated by Penman-Monteith equation. The maximum temperatures are observed to be more effective than the other meteorological variables on the evapotranspiration values calculated by the calibrated Hargreaves-Samani equation for crop water requirements in the Mediterranean Region.

Özet

Penman-Monteith formülü, referans (çim) evapotranspirasyon (ET0) değerlerinin hesaplanmasında tutarlı ve sağlıklı sonuçlar vermesi sebebiyle literatürde en çok kullanılan eşitliktir. Penman-Monteith formülünde referans evapotranspirasyon değerini etkileyen bağımsız değişkenler olarak solar radyasyon (Rs), hava sıcaklığı (T), rüzgâr hızı (U2), ve bağıl nem (RH) gibi meteorolojik veriler kullanılmaktadır. PenmanMonteith eşitliğiyle evapotranspirasyon değerinin hesaplanmasının biraz karışık olmasından ve bu eşitliğin fazla sayıda tanımlayıcı meteorolojik veriye ihtiyaç duymasından dolayı, yeterli veri olmadığı durumlarda onun yerine Hargreaves-Samani eşitliği kullanılmaktadır. Bu çalışmada nem oranının yüksek olduğu Akdeniz Bölgesine ait 38 adet meteoroloji istasyonunda ölçülmüş maksimum sıcaklık, minimum sıcaklık, maksimum nem ve minimum nem verileri kullanılarak Hargreaves-Samani eşitliği kalibre edilmiştir. Bu çalışmanın sonucunda maksimum sıcaklık, minimum sıcaklık, maksimum nem ve minimum nem verileriyle kalibre edilmiş eşitlikler ile elde edilen evapotranspirasyon değerlerinin Penman-Monteith formülü ile hesaplanan değerlere yakın sonuçlar verdiği tespit edilmiştir. Akdeniz Bölgesindeki bitki su ihtiyacının kalibre edilmiş Hargreaves-Samani eşitliği ile hesaplanmasında maksimum sıcaklık verisinin diğer meteorolojik verilere kıyasla daha etkili olduğu görülmüştür

Keywords: Referans evapotranspirasyon, kalibrasyon, Penman-Monteith, Hargreaves-Samani